Question

Danielle is playing the newest app on her phone, Algebra City Defense. Earlier in the game, you and Danielle helped the Mathonauts defend the city against a giant, three-headed monster. After defeating the monster, the game advances to Level Two! You and Danielle must help the Mathonauts blast off to their Interstellar Headquarters.

1. Before blast-off, the Mathonauts must set the trajectory of their ship. Create a linear equation with a positive slope to be your original trajectory.
@mertsj @campbell_st @iambatman @whpalmer4 @Nnesha @bubby

Answer 1

What does it mean by "linear equation"?"

Answer 2

idk thats all it says

Answer 3

Linear means line so linear equation is an equation whose graph is a line.

Answer 4

okay so how would i create my own line

Answer 5

linear equation*

Answer 6

You have probably been studying lines and their equations in your class. Is that right?

Answer 7

yea

Answer 8

So you have learned that y = mx + b is the equation of a line, haven't you?

Answer 9

yes

Answer 10

And what is the slope in the equation y = mx+b?

Answer 11

m

Answer 12

So your problem says to "create a linear equation with positive slope"

Answer 13

would this be a possible equation y=3x+4?

Answer 14

So make up the equation of a line where m is some positive number. You get to choose.

Answer 15

That would be a fine example of a linear equation with positive slope.

Answer 16

then it says
After blast-off, the sensors have picked up an incoming meteor. The Mathonauts frantically start preparing for impact. If the linear equation of the meteor’s path is known, describe to the captain how to solve where your equation from question 1 and the meteor’s path will cross. Explain any possible methods used in discovering a solution.

Answer 17

what is all the missing stuff in that post?

Answer 18

there isn't anything missing just ignore it idk why that happened

Answer 19

What it is saying is this:
You know the path of the rocket ship: y = 3x+4
You know the path of the meteor.
What point do they have in common because if they are at the same spot, they will collide. You have learned at least two methods of solving a system of linear equations.
One method is substitution and the other is elimination.
You may have also learned Kramer's rule.

Answer 20

so what would i do in order to find that? I'm so confused

Answer 21

The problem says that you are to tell the captain how to solve the system.

Answer 22

okay and how do i solve it?

Answer 23

Since your equation is y = 3x+4, I would tell the captain to replace y in the meteor's equation with 3x+4 and solve the equation for x.
Then after he finds x, use the equation y = 3x+4 again. Replace x with the value he found and solve for y. Then he will know where the collision will occur and he can change course.

Answer 24

It doesn't say to solve the problem. It says to tell the captain how to solve the problem.

Answer 25

Having survived the meteor impact, thanks to some last-minute evasive maneuvers, the Mathonauts now set their sights on their Interstellar Headquarters. The Interstellar Headquarters orbits the Earth based on the equation y^2 + x^2 = 40,000. Using the original trajectory of the ship and complete sentences, explain to the pilot how to find where the ship’s path will cross the Interstellar Headquarters’s path.

Answer 26

dont mind the questions in the middle

Answer 27

The same way. Replace y with 3x+4 and solve for x. Then use that value to find y.

Answer 28

While docked, the captain wants to resupply the ship’s missiles and ray-guns. You will need to explain to the captain what information you must know and how that can be used to determine the number of missiles and ray-guns to fill the ship and use all the batteries.
* The ship can hold only 15 weapons total and only has 45 batteries.
* The missiles and ray-guns each require different amounts of batteries to operate.

Answer 29

almost done sorry

Answer 30

still there @Mertsj

Answer 31

There seems to be some information missing.

Answer 32

thats what its says for that question

Answer 33

We can write missiles + ray guns = 15
but we don't know how many batteries a missile requires or how many batteries a ray guy requires.

Answer 34

Oh, I see. That is the information you must tell the captain that you need.

Answer 35

yea, so what should i write?

Answer 36

What are you going to tell the captain you need to know?

Answer 37

ik the original trajectory?

Answer 38

but we don't know how many batteries a missile requires or how many batteries a ray guy requires.

Answer 39

That is what we need to know.

Answer 40

* The ship can hold only 15 weapons total and only has 45 batteries.
* The missiles and ray-guns each require different amounts of batteries to operate.

Answer 41

so what would the answer be to that question?

Answer 42

Question from the problem: "explain to the captain what information you must know and how that can be used to determine the number of missiles and ray-guns to fill the ship and use all the batteries"

Answer 43

Answer to the question: Mr. Captain, sir, I need to know how many batteries a missile requires. Also, sir, I need to know how many batteries a ray gun requires.

Answer 44

Before departing the Interstellar Headquarters, the ship’s navigator begins to plan the next trip. She uses a map with their current trajectory already graphed on it. There is also a table that has coordinate points of a satellite that the Mathonauts must intercept. Explain to the navigator how she can use the graph and table to find where they will intercept the satellite. Assume the path of the satellite is linear. Use the coordinates to create an equation representing the path of the satellite. Explain the process and show how to find the point of intersection algebraically.

Answer 45

@Mertsj

Answer 46

I cannot open that link.

Answer 47

can u open it now? @mertsj

Answer 48

im so lost....

Answer 49

@jdoe0001 @zepdrix